Detectives investigating an "execution-style" murder in Leeds are continuing to speak to the victim's family.
Mr Clarke's body was discovered by his teenage stepson
The body of Richard Clarke, 32, was discovered by his 14-year-old stepson at his Moorland Avenue home on 29 July.
He had been shot once in the head as he slept next to his girlfriend, but there were no signs of any forced entry.
Det Supt Steve Fear said officers had been speaking to the 34-year-old and carrying out lengthy video interviews with her two youngest sons.
Specially-trained family liaison officers were continuing to support the woman and her three teenage sons, he added.
"This is a painstaking process that could take some time, but is the most appropriate way of extracting the fullest information from them about what happened that night," Mr Fear said.
"All of them, particularly Richard Clarke's partner, remain traumatised by the events of last Thursday, but they are able to give us some detail."
Mr Fear, who is leading the investigation, revealed that officers searched one of his former addresses on Royal Park Avenue in Hyde Park, Leeds, on Thursday.
He said he believed the answer to identifying Mr Clarke's killer was in the Hyde Park community.
"Someone living there does know something about Richard Clarke's murder," Mr Fear added.
"I'd like to appeal to them to come forward in confidence and speak to us, no matter how small they think this information is. You could have the crucial link."
Officers have spoken to more than 300 residents so far and house-to-house inquiries continue.